Global existence and blow up for a class of pseudo-parabolic equations with logarithmic nonlinearity

Abstract

In this paper, we discuss the initial–boundary value problem for a class of pseudo-parabolic equations with logarithmic nonlinearity ut−aΔut−Δu+bu=|u|p−2ulog|u|. By the method of Galerkin approximation, we obtain the global existence of weak solutions with low initial energy and critical initial energy J(u0)≤din the case of 1<p<2. What is more, we discuss the finite time blow up of weak solutions, and the ground-state solution of the corresponding steady-state equation under the condition of 2<p<2∗.

Keywords

• Pseudo-parabolic equation
• Global existence
• Blow-up
• Ground-state solution